You're on the right track with your calculations, but you're missing a few key considerations and potential limitations. Here's a breakdown

What you're correct about:
Ohm's Law applies

The fundamental principle is correct. You need to stay within the voltage budget of your power supply, considering the total loop resistance and the desired current.

Wire resistance matters

The resistance of the wire does contribute to the total loop resistance and will limit the distance. Your calculation of the resistance per kilometer of 18AWG is reasonable.

Voltage Drop Matters

You're correct that the voltage drop across the loop resistance needs to be less than the voltage provided by the power supply.

What you're missing



Receiver Voltage Requirements (Burden Voltage)

Your receiver (e.g., PLC input) doesn't just act as a resistor. It requires a minimum voltage across it to properly read the 4-20mA signal. This is often called the "burden voltage" or "compliance voltage." The burden resistor is in the receiver. Your receiver might have a 250-ohm burden resistor, but also needs at least 5V across it to function correctly. You must account for this voltage drop in your calculations.



Transmitter Loop Voltage

Transmitters also require a minimum voltage to work correctly. This is often called the "loop voltage," "compliance voltage," or "minimum operating voltage." This is the voltage that the transmitter needs to be able to drive the current to a certain level. The transmitter needs to be able to drive the current up to 20mA, so you should size your loop to have some headroom above the minimum transmitter loop voltage at 20mA.

Practical Safety Margins

You should not run right up to the limit of your power supply. You want a safety margin for voltage fluctuations, component tolerances, and potential unexpected resistance increases. A 10-20% margin is good practice.

Inductive Load (Cable Inductance)

Long wires act as inductors. While not a major factor in a steady 4-20mA signal, inductance can affect the response time and stability of the loop, especially with fast-changing signals. This is usually only a concern at very long distances or with fast update rates.

Capacitive Load (Cable Capacitance)

Long wires also act as capacitors. This capacitance can slow down signal changes and, in extreme cases, cause instability. Again, usually only a concern at very long distances or with fast update rates.

Noise Pickup

Long wires act as antennas. They can pick up electrical noise from surrounding equipment (motors, fluorescent lights, etc.). This noise can corrupt the 4-20mA signal. Twisted pair shielded cable is essential for long runs to minimize noise pickup. Proper grounding is also critical.

Common Mode Voltage

A current loop is typically floating. This means that the transmitter is floating at some arbitrary voltage relative to ground. If the voltage drifts too far, it could cause problems for the equipment connected to the loop.

Regulatory Requirements

Some industries (e.g., intrinsically safe applications) have strict limits on cable length and inductance/capacitance, regardless of your voltage calculations.

How to Calculate More Accurately


Determine Component Requirements



Power Supply Voltage (Vsupply)

Your supply voltage (e.g., 24V).

Receiver Burden Resistance (Rreceiver)

Typically 250 ohms or 500 ohms.

Receiver Minimum Burden Voltage (Vreceiver_min)

Check the PLC/receiver specifications. This is the minimum voltage required across the receiver to read the 4-20mA signal accurately. This is often around 3-5V.

Transmitter Minimum Loop Voltage (Vtransmitter_min)

Check the transmitter's specifications. This is the minimum voltage the transmitter needs to operate correctly at 20mA.

Maximum Desired Current (Imax)

20mA (0.02A)2.

Calculate Maximum Allowable Loop Resistance

First, calculate the voltage drop across the receiver at the maximum current: `Vreceiver = Imax Rreceiver` Example: `Vreceiver = 0.02A 250 ohms = 5V` Then, determine the remaining voltage available for the transmitter and the cable: `Vavailable = Vsupply - Vreceiver` Example: `Vavailable = 24V - 5V = 19V` Then, subtract the transmitter voltage requirement: `Vavailable_cable = Vavailable - Vtransmitter_min` Example: `Vavailable_cable = 19V - 8V = 11V` (assuming transmitter needs 8V) Now, calculate the maximum allowable loop resistance for the cable: `Rcable_max = Vavailable_cable / Imax` Example: `Rcable_max = 11V / 0.02A = 550 ohms`3.

Calculate Maximum Cable Length

Determine the resistance per kilometer of your wire (one way). Double this for the loop. Example: 42 ohms/km (as you calculated) Divide the maximum allowable cable resistance by the resistance per kilometer: `Cable_Length_max = Rcable_max / (wire resistance per km)` Example: `Cable_Length_max = 550 ohms / (42 ohms/km) = 13.1 km`

Example with Realistic Numbers



Vsupply

24V

Rreceiver

250 ohms

Vreceiver_min

3V (This is required for the receiver to function)

Vtransmitter_min

8V (Minimum voltage for the transmitter to operate correctly)

Imax

0.02A (20mA)

Wire Resistance

42 ohms/km (18AWG, loop resistance)1.

Vreceiver

0.02A 250 ohms = 5V2.

Vavailable

24V - 5V = 19V3.

Vavailable_cable

19V - 8V = 11V4.

Rcable_max

11V / 0.02A = 550 ohms5.

Cable_Length_max

550 ohms / (42 ohms/km) = 13.1 km

How to Extend the Range



Higher Voltage Power Supply

Yes, increasing the power supply voltage allows for more voltage drop across the cable. However, ensure all devices in the loop can handle the higher voltage. You also need to consider safety.

Lower Resistance Wire

Using a larger gauge wire (e.g., 16AWG, 14AWG) significantly reduces the resistance per kilometer, allowing for longer runs.

Repeaters/Isolators

These devices essentially create separate 4-20mA loops, isolating the original signal and re-transmitting it. They also provide isolation, which is important in many industrial applications.

Fiber Optic Conversion

For extremely long distances or high-noise environments, convert the 4-20mA signal to fiber optic.

Important Considerations for Long Runs



Cable Type

Use twisted-pair shielded cable specifically designed for instrumentation. The shield should be properly grounded at one end only (typically at the control panel) to avoid ground loops.

Grounding

Proper grounding is critical to minimize noise pickup. Avoid ground loops. Consult with a qualified electrician for proper grounding practices.

Surge Protection

Protect your equipment from voltage surges (lightning, power surges) with surge protectors at both ends of the loop, especially in outdoor or exposed environments.

Calibration

Long runs can introduce slight errors due to resistance changes with temperature. Periodic calibration may be required.

In summary: While your basic Ohm's law calculation is a good starting point, you need to consider the voltage requirements of the transmitter and receiver, the practical limitations of wire inductance and capacitance, and noise considerations when designing a long-distance 4-20mA loop. Using a higher voltage supply or larger gauge wire can help, but proper cabling, grounding, and noise mitigation techniques are essential for reliable performance. Flag for review